The unification of quantum mechanics and general relativity remains among the most profound challenges in fundamental physics. Here we investigate a novel quantum probe of strong-field gravity: the gravitomagnetic Aharonov-Bohm (AB) effect for Cooper pairs propagating in Kerr spacetime. The frame-dragging induced by a rotating black hole (BH) generates an effective vector potential through the off-diagonal metric component $g_{tϕ}$, which couples to the macroscopic phase of the superconducting condensate. We derive the gauge-invariant AB phase shift $Δθ= (4πm^* Ma/\hbar)(1/r_2 - 1/r_1)$ for an interferometer with arms at radii $r_1$ and $r_2$, where $m^* = 2m_e$ is the Cooper pair mass and $a$ is the BH spin parameter. Remarkably, the predicted phases reach $|Δθ| \sim 10^{24}$ radians for Sgr~A* and $\sim 10^{27}$ radians for M87*, reflecting the enormous gravitomagnetic flux near supermassive BHs. We analyze the dependence on interferometer geometry, demonstrate that tidal disruption of Cooper pairs is negligible at distances $r \gtrsim 10\,r_s$, and establish connections to the geometric Berry phase. Although direct experimental realization remains beyond current technology due to the vast distances involved, our framework provides quantitative predictions linking quantum coherence to spacetime curvature, complementing recent observations of gravitational AB phases in atom interferometry.
Gravitational Aharonov-Bohm effect: theory and experiment
School of Science, Sun Yat-Sen University（中山大学科学学院）；Dipartimento di Fisica, Università di Cagliari（卡利亚里大学物理系）；I.N.F.N, Sezione di Cagliari（意大利国家核物理研究所卡利亚里分部）
The impact of the orbital decay of the LAGEOS satellites on the frame-dragging tests
激光跟踪大地测量卫星LAGEOS、LAGEOS II和LARES目前除其他外用于测量旋转地球重力磁场中的广义相对论性Lense-Thirring效应，希望对爱因斯坦引力理论的这种预测提供比现有的预测更准确的检验。长期衰减$\dot a$的半长轴$a$的这种航天器，最近在一个独立的方式测量到$σ_{\dot a}\approx 0.1-0.01$ m yr $^{-1}$的精度水平，可能间接影响拟议的相对论实验，通过其与经典的轨道进动引起的地球的扁率$J_2$。\textcolor{black}{Indeed,}由于电流测量误差$σ_{\dot a}$引起的系统偏差与预期的相对论信号本身具有相同的数量级，甚至大于预期的相对论信号本身;此外，它随着分析的时间跨度$T$线性增长。\textcolor{black}{Therefore, the parameter-fitting algorithms must be properly updated in order to suitably cope with such a new source of systematic uncertainty. Otherwise,}在测量LAGEOS系列卫星的轨道衰减方面需要改进一到两个数量级，以便将这种系统不确定性的来源减少到Lense-Thirring特征的百分之几。
Mercury and frame-dragging in light of the MESSENGER flybys: conflict with general relativity, poor knowledge of the physical properties of the Sun, data reduction artifact, or still insufficient observations?
广义相对论利用日震学中太阳的角动量S = 190 x 10^39 kg m^2 s^-1，预测水星近日点经度的兰斯-瑟林岁差为-2.0毫角秒/世纪（在天体赤道参考系中计算）。在4-σ水平上，它与标准牛顿/爱因斯坦岁差的0.4 +/- 0.6毫角秒/世纪修正值不一致，只要后者完全归因于标架拖曳。补充岁差是最近用INPOP 10a星历表与一个长行星数据记录（1914-2010年）进行全球拟合确定的，其中包括2008-2009年从信使号航天器收集的3个数据点。INPOP 10a模型根本不包括太阳重力磁场，因此它的特征可能在数据简化过程中被部分删除。另一方面，Lense-Thirring进动可能在一定程度上被竞争进动所抵消，这些竞争进动是由太阳四极质量矩和PPN参数β进入Schwarzschild类1 PN进动的小错误建模引起的，两者都是在INPOP 10a中建模的。相反，水星本身的扁率对其近日点的影响可以忽略不计。最大的单个小行星和小行星环的错误模型行为也是如此。未来对目前正在进行的信使号任务的更多观测结果的分析将进一步阐明这一问题，如果得到证实，可能会挑战我们目前对目前公认的引力定律和/或太阳物理特性的看法。
